Applying Lanchester's linear law to model the Ardennes campaign

A simple method to fit the Lanchester’s linear model for Ardennes Champaign

“…Ip Section 4, numerical example from the historical data of Ardennes Champaign shows the superiority of our solution over the solutions of Bracken [1]. From the relative error between our result and Chen and Chu [2] we know that our result is accurate enough. In Section 5 we summarize the findings in this paper and give hints for future study .…”

“…First we recall the Lanchester's linear law with tactical factor from Chen and Chu [2] ..... (1) Given k, their procedure is to obtain the local critical points of SSRk(a, b, d), under the restrictions a, band d are all positive. Their method involves complicate partial derivative computation, moreover, the uniqueness for the solution is only verified by the example con structed from the historical data.…”

“…Those complicate computation algorithms suggested by Lan et al [3] or Chen and Chu [2] become insufficient .. Hence, in this note, we try to obtain a simple method to appraise the attrition.rate and the tactical factor for the Lanchester's linear law.…”

“…Mter length computation and with the help of a computer program to solve a polynomial of twelve degree, they showed that the system of first order conditions has a unique solution, which is the genuine minimum solution. Recently, Chen and Chu [2] examined the corre sponding problem with the traditional Lanchester's linear law, in which they derived a sufficient condition to guarantee the existence and uniqueness of the solution for the system of first-order conditions, but their solution procedure also requires sophisticated computation.…”

“…Using the historical data of the famous Ardennes Champaign in the Second World War, we show that our approximation is acceptable with a relative small error. Rest of the paper is organized as follows: In Section 2 we give the assumptions and notation used in this paper that is adopted directly from the papers of Bracken [1], Lan et al [3] and Chen and Chu [2]. Section 3 is the core of the paper that deals with mathematical modeling.…”